Question

Stuck on this please help

Answer 1

Answer:

The answers are given below.

Step-by-step explanation:

7. Simplified Fractions/Integers:

a. $(25)^{\frac{-3}{2}}$

= $(5^2)^{\frac{-3}{2}}$

= $5^{-3}$

= $\frac{1}{5^3} = \frac{1}{125}$ is the required answer.

b. $\bigg ( \frac{1}{7} \bigg )^{2}$

= $\bigg( \frac{1}{7^2} \bigg)$

= $\frac{1}{49}$ is the required answer.

c. $\bigg ( \frac{1}{7} \bigg) ^{-3}$

= $\bigg ( \frac{1}{7^{-3}} \bigg )$

= $7^{3}$ = 343 is the required answer.

8. Simplified Fractions:

a. $\bigg( \frac{27}{8} \bigg ) ^{\frac{2}{3}}$

= $\bigg ( \frac{3^3}{2^3} \bigg ) ^{\frac{2}{3}}$

= $\bigg ( \frac{3}{2} \bigg) ^2$

$= \frac{9}{4}$ is the required answer.

b. $\bigg ( \frac{4}{25} \bigg)^{\frac{-3}{2}}$

= $\bigg ( \frac{2^2}{5^2} \bigg)^{\frac{-3}{2}}$

= $\bigg ( \frac{2^{-3}}{5^{-3}} \bigg )$

= $\bigg( \frac{5^3}{2^3} \bigg )$

= $\frac{125}{8}$ is the required answer.

9. Index Forms:

a. √3

= $3^{\frac{1}{2}}$ is the required answer.

b. ∛3

= $3^{\frac{1}{3}}$ is the required answer.

c. $\sqrt[6]{2}$

= $2^{\frac{1}{6}$ is the required answer.

d. $\sqrt{5^3}$

= $5^{\frac{3}{2}}$ is the required answer.

e. $\frac{1}{(\sqrt[3]{5})^2}$

= $\frac{1}{5^{\frac{2}{3}}}$

= $5^{\frac{-2}{3}}$ is the required answer.